AAAI 2026 Papers

AAAI Conference on Artificial Intelligence

Decision breakdown

4,436papers

Counted from the official paper list; may differ slightly from the number the conference announced.

  • Other / unlabeled
    4,436100.0%

Top 10 topics (click to filter)

No topic data yet.

Trends for all 207 research topics

Browse all papers

ENHash: Error Notebook-Guided Fine-Grained Learning for Unsupervised Cross-Modal Hashing

Hao Fu, Zebing Yao, Chuangchuang Tan, Guanghua Gu

Expand abstract

Without manual annotations, unsupervised cross-modal hashing (UCMH) aims to achieve efficient clustering and retrieval by leveraging data interrelationships. However, the retrieval accuracy is constrained by two main aspects: 1) insufficient exploration of data relationships; 2) existing knowledge mining strategies are not well aligned with the architectural properties of multilayer perceptrons. Through summary and error analysis, the human brain is able to achieve fast learning through experience and minimal data. Inspired by this cognitive process, we propose a novel Error Notebook strategy, named ENHash, to more effectively capture similarity information between multi-modal data for fine-grained unsupervised clustering. Firstly, simulating the human process of summarizing experiences, ENHash gradually integrates the information from each batch into a global clustering representation. Secondly, drawing upon human error analysis capabilities, ENHash utilizes the summarized experiences to identify and record incorrectly predicted hash codes. Finally, by leveraging the knowledge derived from this analysis, ENHash guides the hash function to learn fine-grained patterns from the errors. To the best of our knowledge, ENHash represents the first attempt at integrating cognitively-inspired mechanisms into fine-grained UCMH optimization paradigms. We evaluate the proposed ENHash against eight state-of-the-art methods on three widely used datasets and one fine-grained cross-modal dataset. Experimental results show that ENHash achieves substantial improvements over existing approaches.

Technical
DeToNATION: Decoupled Torch Network-Aware Training on Interlinked Online Nodes

Mogens Henrik From, Jacob Nielsen, Lukas Galke, Peter Schneider-Kamp

Expand abstract

Training large neural network models requires extensive computational resources, often distributed across several nodes and accelerators. Recent findings suggest that it may be sufficient to only exchange the fast moving components of the gradients, while accumulating momentum locally (Decoupled Momentum, or DeMo). However, DeMo assumes that models fit on a single accelerator. We relax this assumption and introduce FlexDeMo, whereby nodes fully shard model parameters locally between different accelerators, while inter-node communication is reduced by synchronizing only fast-moving components instead of the full gradients -- resulting in a hybrid sharded data parallel training strategy. We further introduce a framework, denoted as DeToNATION, that generalizes DeMo, FlexDeMo, and other popular distributed training schemes such as DiLoCo -- introducing new variations of replication schemes and challenging choices made in DeMo. Our results across language and vision domains show that FlexDeMo attains similar validation loss as hybrid sharded data parallel training employing AdamW and full gradient synchronization, while being substantially faster. FlexDeMo is thus a promising distributed training scheme for the largest machine learning models.

Technical
Statistical Learning Theory for Distributional Classification

Christian Fiedler

Expand abstract

In supervised learning with distributional inputs in the two-stage sampling setup, relevant to applications like learning-based medical screening or causal learning, the inputs (which are probability distributions) are not accessible in the learning phase, but only samples thereof. This problem is particularly amenable to kernel-based learning methods, where the distributions or samples are first embedded into a Hilbert space, often using kernel mean embeddings (KMEs), and then a standard kernel method like Support Vector Machines (SVMs) is applied, using a kernel defined on the embedding Hilbert space. In this work, we contribute to the theoretical analysis of this latter approach, with a particular focus on classification with distributional inputs using SVMs. We establish a new oracle inequality and derive consistency and learning rate results. Furthermore, for SVMs using the hinge loss and Gaussian kernels, we formulate a novel variant of an established noise assumption from the binary classification literature, under which we can establish learning rates. Finally, some of our technical tools like a new feature space for Gaussian kernels on Hilbert spaces are of independent interest.

Technical
EM-KD: Distilling Efficient Multimodal Large Language Model with Unbalanced Vision Tokens

Ze Feng, Sen Yang, Boqiang Duan, Wankou Yang, Jingdong Wang

Expand abstract

Efficient Multimodal Large Language Models (MLLMs) compress vision tokens to reduce resource consumption, but the loss of visual information can degrade comprehension capabilities. Although some priors introduce Knowledge Distillation to enhance student models, they overlook the fundamental differences in fine-grained vision comprehension caused by unbalanced vision tokens between the efficient student and vanilla teacher. In this paper, we propose EM-KD, a novel paradigm that enhances the Efficient MLLMs with Knowledge Distillation. To overcome the challenge of unbalanced vision tokens, we first calculate the Manhattan distance between the vision logits of teacher and student, and then align them in the spatial dimension with the Hungarian matching algorithm. After alignment, EM-KD introduces two distillation strategies: 1) Vision-Language Affinity Distillation (VLAD) and 2) Vision Semantic Distillation (VSD). Specifically, VLAD calculates the affinity matrix between text tokens and aligned vision tokens, and minimizes the smooth L1 distance of the student and the teacher affinity matrices. Considering the semantic richness of vision logits in the final layer, VSD employs the reverse KL divergence to measure the discrete probability distributions of the aligned vision logits over the vocabulary space. Comprehensive evaluation on diverse benchmarks demonstrates that EM-KD trained model outperforms prior Efficient MLLMs on both accuracy and efficiency with a large margin, validating its effectiveness. Compared with previous distillation methods, which are equipped with our proposed vision token matching strategy for fair comparison, EM-KD also achieves better performance.

Technical
Adaptive and Asymptotic Mean-based Subclass Discriminant Analysis

Yuzhe Feng, Yunlong Gao, Feiping Nie

Expand abstract

Traditional Discriminant analysis (DA) is one of the classical supervised learning algorithms to reduce the dimensionality of data with Gaussian assumption. Since the unique class mean in traditional DA is intractable to estimate the non-Gaussian distrbution of data, some existing DA algorithms based on the clustering criterion focus on learning multiple means in each class so as to address the non-Gaussian issue. The clustering-based DA inevitably involved the constraint optimization problem to learn multiple means, which may lead to the locally optimal solution. To address these issues, inspired by the smooth approximation theory and the concept of Kolmogorov mean, this paper explores an unconstraint function with asymptotic property as an alternative proxy to clustering-based DA algorithms. Thus the derived DA algorithm, i.e., adaptive and asymptotic mean-based subclass discriminant analysis (AASDA), which not only leverages multiple means to represent different subclasses in same class but also adaptively and asymptotically learns the similar mean for each sample in the learned optimal subspace via the gradient-based optimizer. The asymptotic analysis of unconstraint function, the gradient analysis and convergence guarantee of proposed criterion verify the effectiveness of AASDA algorithm. Its merits are thoroughly assessed on a suite of synthetic and real world data experiments.

Technical
Behavior Tokens Speak Louder: Disentangled Explainable Recommendation with Behavior Vocabulary

Xinshun Feng, Mingzhe Liu, Yi Qiao, Tongyu Zhu, Leilei Sun, Shuai Wang

Expand abstract

Recent advances in explainable recommendation have explored the integration of language models to analyze natural language rationales for user–item interactions. Despite their potential, existing methods often rely on ID-based representations that obscure semantic meaning and impose structural constraints on language models, thereby limiting their applicability in open-ended scenarios. These challenges are intensified by the complex nature of real-world interactions, where diverse user intents are entangled and collaborative signals rarely align with linguistic semantics. To overcome these limitations, we propose BEAT, a unified and transferable framework that tokenizes user and item behaviors into discrete, interpretable sequences. We construct a behavior vocabulary via a vector-quantized autoencoding process that disentangles macro-level interests and micro-level intentions from graph-based representations. We then introduce multi-level semantic supervision to bridge the gap between behavioral signals and language space. A semantic alignment regularization mechanism is designed to embed behavior tokens directly into the input space of frozen language models. Experiments on three public datasets show that BEAT improves zero-shot recommendation performance while generating coherent and informative explanations. Further analysis demonstrates that our behavior tokens capture fine-grained semantics and offer a plug-and-play interface for integrating complex behavior patterns into large language models.

Technical
Federated Incomplete Multi-View Clustering with Tensorized Low-Rank Constraint

Wei Feng, Danting Liu, Qianqian Wang, Mengping Jiang, Bin Liu

Expand abstract

Federated Multi-View Clustering has gained increasing attention for its ability to discover complementary clustering structures of distributed multi-view data while preserving data privacy. However, real-world clients often only have access to partial views, and the view incompleteness poses great challenges to federated multi-view feature fusion to exploit consistent and complementary information. Moreover, efficiency is highly expected in federated scenarios due to the limited resources of each client. To alleviate these issues, we propose Federated Incomplete Multi-View Clustering with Tensorized Low-Rank Constraint (FIMVC-TLRC), which incorporates anchors to improve efficiency and is able to address prevalent view incompleteness issue in federated scenarios. FIMVC-TLRC aligns the local anchor graphs and employs a tensorized low-rank constraint based on the tensor Schatten p-norm to enforce the consistency of the data representations learned by each client. Besides, a federated optimization framework is developed to jointly optimize the construction and alignment of anchor graphs, thus enabling collaborative and privacy-preserving training. Experimental results on multiple datasets demonstrate its effectiveness.

Technical
WIET: Harmonizing Group-aware Model Weighting and Worker Allocation for Ensemble Temporal Prediction MaaS

Binbin Feng, Shikun He, Yingxin Wang, Pengwei Wang, Xiang Gao, Zhijun Ding

Expand abstract

Ensemble Temporal Prediction Model-as-a-Service (ETP-MaaS) has become crucial in fields like financial modeling and cloud monitoring. Existing solutions fail to co-optimally address a two-fold challenge of dynamic collaboration and heterogeneity, treating models as independent entities and employing simplistic worker allocation rules. However, at the model level, data volatility means that optimal performance requires identifying and weighting constantly shifting subgroups of base models, not just individual ones; at the system level, these model groups must be efficiently mapped to a pool of heterogeneous and dynamically available workers. To this end, we introduce WIET, an efficient ETP-MaaS system that co-optimizes model weighting and worker allocation. For adaptive weighting, WIET identifies evolving group behaviors among base models and propose a novel group temporal locality-enhanced weighting method. Additionally, WIET develops an efficient, multi-dimensional worker allocation method powered by hybrid heuristic optimization, effectively reducing bottlenecks and resource waste. Experiments show WIET consistently outperforms state-of-the-art methods in terms of accuracy, latency, and resource usage across various workloads and tasks.

Technical
Goal-Oriented Time-Series Forecasting: Foundation Framework Design

Luca-Andrei Fechete, Mohamed Sana, Fadhel Ayed, Nicola Piovesan, Wenjie Li, Antonio De Domenico, Tareq Si Salem

Expand abstract

Conventional time-series forecasting methods typically aim to minimize overall prediction error, without accounting for the varying importance of different forecast ranges in downstream applications. We propose a training methodology that enables forecasting models to adapt their focus to application-specific regions of interest at inference time, without retraining. The approach partitions the prediction space into fine-grained segments during training, which are dynamically reweighted and aggregated to emphasize the target range specified by the application. Unlike prior methods that predefine these ranges, our framework supports flexible, on-demand adjustments. Experiments on standard benchmarks and a newly collected wireless communication dataset demonstrate that our method not only improves forecast accuracy within regions of interest but also yields measurable gains in downstream task performance. These results highlight the potential for closer integration between predictive modeling and decision-making in real-world systems.

Technical
To Align or Not to Align: Strategic Multimodal Representation Alignment for Optimal Performance

Wanlong Fang, Tianle Zhang, Alvin Chan

Expand abstract

Multimodal learning often relies on aligning representations across modalities to enable effective information integration—an approach traditionally assumed to be universally beneficial. However, prior research has primarily taken an observational approach, examining naturally occurring alignment in multimodal data and exploring its correlation with model performance, without systematically studying the direct effects of explicitly enforced alignment between representations of different modalities. In this work, we investigate how explicit alignment influences both model performance and representation alignment under different modality-specific information structures. Specifically, we introduce a controllable contrastive learning module that enables precise manipulation of alignment strength during training, allowing us to explore when explicit alignment improves or hinders performance. Our results on synthetic and real datasets under different data characteristics show that the impact of explicit alignment on the performance of unimodal models is related to the characteristics of the data: the optimal level of alignment depends on the amount of redundancy between the different modalities. We can find an optimal alignment strength that balances modality-specific signals and shared redundancy in the mixed information distributions. This work can help practitioners on when and how to enforce alignment for optimal unimodal encoder performance.

Technical
Graph Domain Adaptation via Homophily-Agnostic Reconstructing Structure

Ruiyi Fang, Shuo Wang, Ruizhi Pu, QIUHAO Zeng, Hao ZHENG, Ziyan Wang, Jiale Cai, Zhimin Mei, Song Tang, Charles Ling, Boyu Wang

Expand abstract

Graph Domain Adaptation (GDA) transfers knowledge from labeled source graphs to unlabeled target graphs, addressing the challenge of label scarcity. However, existing GDA methods typically assume that both source and target graphs exhibit homophily, leading existing methods to perform poorly when heterophily is present. Furthermore, the lack of labels in the target graph makes it impossible to assess its homophily level beforehand. To address this challenge, we propose a novel homophily-agnostic approach that effectively transfers knowledge between graphs with varying degrees of homophily. Specifically, we adopt a divide-and-conquer strategy that first separately reconstructs highly homophilic and heterophilic variants of both the source and target graphs, and then performs knowledge alignment separately between corresponding graph variants. Extensive experiments conducted on five benchmark datasets demonstrate the superior performance of our approach, particularly highlighting its substantial advantages on heterophilic graphs.

Technical
Towards Illumination-Aware Restoration of Metalens-Captured Images: A New Dataset and a Strong Baseline

Fen Fang, Xinan Liang, Muli Yang, Jinghong Zheng, Tobias Mass, Ying Sun, Xulei Yang, Xuewu Xu, Zhengguo Li

Expand abstract

Metalenses offer compelling advantages such as lightweight and ultra-thin design, making them promising alternatives to conventional lenses. However, their widespread adoption is hindered by image quality degradation caused by chromatic and angular aberrations. To mitigate this, restoration processes are often necessary to recover high-quality RGB images from metalens-captured inputs. While recent deep learning-based restoration methods show promise, they typically (1) blur or distort peripheral regions, or (2) fail entirely under unseen illumination conditions. To advance metalens image restoration, we introduce IlluMeta---the first and largest real-world, illumination-aware metalens image dataset—captured across diverse lighting environments. In addition, we propose a novel end-to-end restoration framework that directs attention to challenging regions and adaptively adjusts to varying illuminations via reinforcement learning. Experiments show that our method can be applied in a plug-and-play manner to enhance existing models, significantly improving image restoration quality, especially under unseen lighting conditions, paving the way for broader real-world deployment of metalens technologies.

Technical
Hierarchical Structure-Property Alignment for Data-Efficient Molecular Generation and Editing

Ziyu Fan, Zhijian Huang, Yahan Li, Xiaowen Hu, Siyuan Shen, Yunliang Wang, Zeyu Zhong, Shuhong Liu, Shuning Yang, Shangqian Wu, Min Wu, Lei Deng

Expand abstract

Property-constrained molecular generation and editing are crucial in AI-driven drug discovery but remain hindered by two factors: (i) capturing the complex relationships between molecular structures and multiple properties remains challenging, and (ii) the narrow coverage and incomplete annotations of molecular properties weaken the effectiveness of property-based models. To tackle these limitations, we propose HSPAG, a data-efficient framework featuring hierarchical structure–property alignment. By treating SMILES and molecular properties as complementary modalities, the model learns their relationships at atom, substructure, and whole-molecule levels. Moreover, we select representative samples through scaffold clustering and hard samples via an auxiliary variational auto-encoder (VAE), substantially reducing the required pre-training data. In addition, we incorporate a property relevance-aware masking mechanism and diversified perturbation strategies to enhance generation quality under sparse annotations. Experiments demonstrate that HSPAG captures fine-grained structure–property relationships and supports controllable generation under multiple property constraints. Two real-world case studies further validate the editing capabilities of HSPAG.

Technical
TFRank: Think-Free Reasoning Enables Practical Pointwise LLM Ranking

Yongqi Fan, Xiaoyang Chen, Dezhi Ye, Jie Liu, Haijin Liang, Jin Ma, Ben He, Yingfei Sun, Tong Ruan

Expand abstract

Reasoning-intensive ranking models built on Large Language Models (LLMs) have made notable progress. However, existing approaches often rely on large-scale LLMs and explicit Chain-of-Thought (CoT) reasoning, resulting in high computational cost and latency that limit real-world use. To address this, we propose TFRank, an efficient pointwise reasoning ranker based on small-scale LLMs. To improve ranking performance, TFRank effectively integrates CoT data, fine-grained score supervision, and multi-task training. Furthermore, it achieves an efficient "Think-Free" reasoning capability by employing a "think-mode switch" and pointwise format constraints. Specifically, this allows the model to leverage explicit reasoning during training while delivering precise relevance scores for complex queries at inference without generating any reasoning chains. Experiments show that TFRank achieves performance comparable to models with four times more parameters on the BRIGHT benchmark, and demonstrates strong competitiveness on the BEIR benchmark. Further analysis shows that TFRank achieves an effective balance between performance and efficiency, providing a practical solution for integrating advanced reasoning into real-world systems.

Technical
MoETTA: Test-Time Adaptation Under Mixed Distribution Shifts with MoE-LayerNorm

Xiao Fan, Jingyan Jiang, Zhaoru Chen, Fanding Huang, Xiao Chen, Qinting Jiang, Bowen Zhang, Xing Tang, Zhi Wang

Expand abstract

Test-time adaptation (TTA) has proven effective in mitigating performance drops under single-domain distribution shifts by updating model parameters during inference. However, real-world deployments often involve mixed distribution shifts---where test samples are affected by diverse and potentially conflicting domain factors---posing significant challenges even for state-of-the-art TTA methods. A key limitation in existing approaches is their reliance on a unified adaptation path, which fails to account for the fact that optimal gradient directions can vary significantly across different domains. Moreover, current benchmarks focus only on synthetic or homogeneous shifts, failing to capture the complexity of real-world heterogeneous mixed distribution shifts. To address this, we propose MoETTA, a novel entropy-based TTA framework that integrates the Mixture-of-Experts (MoE) architecture. Rather than enforcing a single parameter update rule for all test samples, MoETTA introduces a set of structurally decoupled experts, enabling specialization along diverse gradient directions. This design allows the model to better accommodate heterogeneous shifts through flexible and disentangled parameter updates. To simulate realistic deployment conditions, we introduce two new benchmarks: potpourri and potpourri+. While classical settings focus solely on synthetic corruptions (i.e., ImageNet-C), potpourri encompasses a broader range of domain shifts—including natural, artistic, and adversarial distortions—capturing more realistic deployment challenges. On top of that, potpourri+ further includes source-domain samples to evaluate robustness against catastrophic forgetting. Extensive experiments across three mixed distribution shifts settings show that MoETTA consistently outperforms strong baselines, establishing new state-of-the-art performance and highlighting the benefit of modeling multiple adaptation directions via expert-level diversity.

Technical
Online Cross-Modal Hashing with Expanding Label Space

Wentao Fan, Chao Zhang, Chunlin Chen, Huaxiong Li

Expand abstract

Due to the continuous increase of multimedia data on the internet, online hashing has garnered considerable attention for handling multi-modal data streams. However, most existing online hashing approaches focus solely on data growth of samples, overlooking the dynamics of classes. In this paper, we simultaneously address the challenges of both sample-level and class-level growth, and propose a novel Online Hashing method with Expanding Label Space (OH-ELS) for cross-modal retrieval. In OH-ELS, multi-modal data arrives continuously, and incoming data may introduce new classes. To avoid catastrophic forgetting, we transfer the historical knowledge at both the sample and class levels. At the sample-level, a small subset of anchor codes from old data are replayed to preserve the similarities between new data and old data. At the class-level, a consistency regularizer is applied to new classifiers to leverage the priors of historical classes. To ensure both efficiency and accuracy, a discrete optimization algorithm is proposed to solve the binary-constrained optimization problem without relaxation. Experimental results illustrate the effectiveness and superiority of OH-ELS in class-incremental cross-modal retrieval compared with the state-of-the-art methods.

Technical
Efficient Multimodal Large Language Model via Dynamic KV Cache Quantization

Jiahao Fan, Chien-Ming Chen

Expand abstract

Multimodal large language models (LMMs) have demonstrated remarkable capabilities across diverse vision-language tasks, including image captioning, visual question answering, and text-image retrieval. However, their computational complexity and memory footprint, particularly in the key-value (KV) cache during inference, pose significant challenges for real-time deployment, especially on resource-constrained devices. In this paper, we propose Dynamic KV Cache Quantization, a novel quantization strategy tailored for multimodal LMMs. Our approach applies per-channel quantization to (K) and per-token quantization to (V), leveraging their respective statistical distributions to optimize precision allocation. Additionally, we introduce an adaptive token and channel recording mechanism that dynamically adjusts quantization parameters based on real-time distribution tracking, effectively mitigating the impact of outliers. To further enhance compression efficiency, we implement fine-grained grouping, which partitions KV tensors into localized subgroups, enabling more adaptive quantization. Experimental results on LLaVA-1.5 (7B/13B) and Qwen-VL across multiple multimodal benchmarks demonstrate that our method significantly outperforms existing KV-cache quantization approaches, achieving a superior trade-off between memory efficiency and model accuracy.

Technical
Decomposing and Composing: Towards Efficient Vision-Language Continual Learning via Rank-1 Expert Pool in a Single LoRA

Zhan Fa, Yue Duan, Jian Zhang, Lei Qi, Wanqi Yang, Yinghuan Shi

Expand abstract

Continual learning (CL) in vision-language models (VLMs) faces significant challenges in improving task adaptation and avoiding catastrophic forgetting. Existing methods usually have heavy inference burden or rely on external knowledge, while Low-Rank Adaptation (LoRA) has shown potential in reducing these issues by enabling parameter-efficient tuning. However, considering directly using LoRA to alleviate the catastrophic forgetting problem is non-trivial, we introduce a novel framework that restructures a single LoRA module as a decomposable Rank-1 Expert Pool. Our method learns to dynamically compose a sparse, task-specific update by selecting from this expert pool, guided by the semantics of the [CLS] token. In addition, we propose an Activation-Guided Orthogonal (AGO) loss that orthogonalizes critical parts of LoRA weights across tasks. This sparse composition and orthogonalization enable fewer parameter updates, resulting in domain-aware learning while minimizing inter-task interference and maintaining downstream task performance. Extensive experiments across multiple settings demonstrate state-of-the-art results in all metrics, surpassing zero-shot upper bounds in generalization. Notably, it reduces trainable parameters by 96.7% compared to the baseline method, eliminating reliance on external datasets or task-ID discriminators. The merged LoRAs retain less weights and incur no inference latency, making our method computationally lightweight.

Technical
Simulation-Driven Railway Delay Prediction: An Imitation Learning Approach

Clément Elliker, Jesse Read, Sonia Vanier, Albert Bifet

Expand abstract

Reliable prediction of train delays is essential for enhancing the robustness and efficiency of railway transportation systems. In this work, we reframe delay forecasting as a stochastic simulation task, modeling state-transition dynamics through imitation learning. We introduce Drift-Corrected Imitation Learning (DCIL), a novel self-supervised algorithm that extends DAgger by incorporating distance-based drift correction, thereby mitigating covariate shift during rollouts without requiring access to an external oracle or adversarial schemes. Our approach synthesizes the dynamical fidelity of event-driven models with the representational capacity of data-driven methods, enabling uncertainty-aware forecasting via Monte Carlo simulation. We evaluate DCIL using a comprehensive real-world dataset from \textsc{Infrabel}, the Belgian railway infrastructure manager, which encompasses over three million train movements. Our results, focused on predictions up to 30 minutes ahead, demonstrate superior predictive performance of DCIL over traditional regression models and behavioral cloning on deep learning architectures, highlighting its effectiveness in capturing the sequential and uncertain nature of delay propagation in large-scale networks.

Technical
FlorE: Integrating Full Lorentz Group and Directional Offsets for Effective Knowledge Graph Embedding

Zehua Duo, Jiang Li, Xiangdong Su, Guanglai Gao

Expand abstract

Knowledge Graph Embedding (KGE) aims to map entities and relationships into a continuous vector space to facilitate reasoning and downstream tasks. Although previous KGE methods based on Euclidean, complex spaces, or hyperbolic spaces have performed well, they still struggle to effectively model Z-Paradox relation patterns which account for a large proportion in each knowledge graph. To address this issue, we propose a novel KGE method **FlorE** which integrates full Lorentz Group and directional offset operation in hyperbolic space for KGE task. Specifically, we incorporates the full Lorentz Group to enable the same relation in knowledge graph (KG) to perform indefinite isometry, thus avoiding the overlapping of entities. Meanwhile, we implement directional offset operation via exponential mapping to transform the relations to the same Lorentz manifold of the entities, thus maintaining geometric consistency for the relations and entities in KG. By integrating these two techniques, FlorE can effectively model the Z-Paradox relation patterns and improve the representation learning ability for KGs. Experiments on the five benchmark datasets demonstrate that our method achieves state-of-the-art performance. For the Z-Paradox relation patterns, the improvement achieves **26.7%**, **15.6%**, **35.4%**, **33.7%**, and **31.5%** on FB15k-237, WN18RR, CoDEx-S, CoDEx-M and CoDEx-L, respectively.

Technical